Ed Gallagher - Title: Improved Concentration Bounds For Gaussian Quadratic Forms.
Random variables taking the form of a sum of weighted non-centralised chi-squareds arise in many applications- in particular, in genomics and medicine. We develop new upper bounds on such variables that are both rapid to compute and significantly tighter than previous bounds.

Daniel Galvin - Title: Knots in S^1×S^2.
A very brief introduction to knot theory in R^3, followed by how we can have knots in a different 3-manifold (S^1 x S^2) and properties that these knots have that normal knots do not.

Leyna May - Curvature on regular graphs.
Curvature is a broad and important concept in geometry, and can be applied to a number of different objects. Introducing the notion of curvature to discrete structures such as graphs or networks leads to interesting results and applications, as well as a classification of graphs with special properties.

Alex Greenen - Title: Study of Force Free Magnetic Fields in a Tube.
This project looked at finding analytic expressions for force free magnetic fields on the solar corona using differential geometry.